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<Paper uid="P95-1029">
  <Title>Using Higher-Order Logic Programming for Semantic Interpretation of Coordinate Constructs</Title>
  <Section position="4" start_page="213" end_page="214" type="intro">
    <SectionTitle>
2 CCG
</SectionTitle>
    <Paragraph position="0"> CCG is a grammatical formalism in which there is a one-to-one correspondence between the rules of composition 1 at the level of syntax and logical form.</Paragraph>
    <Paragraph position="1"> Each word is (perhaps ambiguously) assigned a category and LF, and when the syntactical operations assign a new category to a constituent, the corresponding semantic operations produce a new LF for that constituent as well. The CCG rules shown in Figure 1 are implemented in the system described 1In the genera\] sense, not specifically the CCG rule for function composition.</Paragraph>
    <Paragraph position="2">  by first-order unification in this paper. 2 3 Each of the three operations have both a forward and backward variant.</Paragraph>
    <Paragraph position="3"> As an illustration of how the semantic rules can be simulated in first-order unification, consider the derivation of the constituent harry found, where harry has the category np with LF harry' and found  is a transitive verb of category (s\np)/np with LF (5) Aobject.Asubject.(found' subject object)  In the CCG formalism, the derivation is as follows: harry gets raised with the &gt; T rule, and then forward composed by the &gt; B rule with found, and the result is a category of type s/rip with LF Az.(found' harry' z). In section 3 it will be seen how the use of abstract syntax allows this to be expressed directly. In first-order unification, it is simulated as shown in Figure 2. 4 The final CCG rule to be considered is the coordination rule that specifies that only like categories can coordinate: 2The type-raising rules shown are actually a simplification of what has been implemented. In order to handle determiners, a system similar to NP-complement categories as discussed in (Dowty, 1988) is used. Although a worthwhile further demonstration of the use of abstract syntax, it has been left out of this paper for space reasons.</Paragraph>
    <Paragraph position="5"> This is actually a schema for a family of rules, collectively called &amp;quot;generalized coordination&amp;quot;, since the semantic rule is different for each case. 5 For example, if X is a unary function, then the semantic rule is (Ta), and if the functions have two arguments, then the rule is (7b). s</Paragraph>
    <Paragraph position="7"> For example, when processing (la), rule (Ta) would</Paragraph>
    <Paragraph position="9"> which is c=-equivalent to (2).</Paragraph>
  </Section>
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